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La ecuación:
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
Ecuación x^2+4=5x
Ecuación x(x^2+2x+1)=6(x+1)
Ecuación 4x+1=-3x+15
Expresar {x} en función de y en la ecuación:
-6*x-20*y=8
13*x-12*y=19
-9*x+11*y=9
-4*x-8*y=-20
Integral de d{x}:
sin3xsin5x
Expresiones idénticas
cos4xcos2x=sin3xsin5x
coseno de 4x coseno de 2x es igual a seno de 3x seno de 5x
Expresiones semejantes
√3(cos4x+1)=2(2-cos4x)cos2x
8*cos(4*x)*cos(2*x)*cos(3*x)=1

cos4xcos2x=sin3xsin5x la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

cos(4*x)*cos(2*x) = sin(3*x)*sin(5*x)

$$\cos{\left(2 x \right)} \cos{\left(4 x \right)} = \sin{\left(3 x \right)} \sin{\left(5 x \right)}$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

                                                                                                                                     /   /pi\\            /   /pi\\                                            /   /pi\\                                                                               /   /pi\\
                                                                                                   /    _____________________\       |cos|--||            |cos|--||        /    _____________________\         |cos|--||        /    _____________________\          /    _____________________\       |cos|--||
  pi   3*pi   pi   pi   3*pi   pi   11*pi   13*pi        / 14____\        /     3/14\              |   /    2/pi\      2/pi\ |       |   \7 /|            |   \7 /|        |   /    2/pi\      2/pi\ |         |   \7 /|        |   /    2/pi\      2/pi\ |          |   /    2/pi\      2/pi\ |       |   \7 /|
- -- - ---- - -- + -- + ---- + -- + ----- + ----- - I*log\-\/ -1 / - I*log\-(-1)    / + -pi - I*log|  /  cos |--| + sin |--| | + atan|-------| + pi - atan|-------| - I*log|  /  cos |--| + sin |--| | + - atan|-------| - I*log|  /  cos |--| + sin |--| | + - I*log|  /  cos |--| + sin |--| | + atan|-------|
  2     14    14   14    14    2      14      14                                                   \\/       \7 /       \7 / /       |   /pi\|            |   /pi\|        \\/       \7 /       \7 / /         |   /pi\|        \\/       \7 /       \7 / /          \\/       \7 /       \7 / /       |   /pi\|
                                                                                                                                     |sin|--||            |sin|--||                                            |sin|--||                                                                               |sin|--||
                                                                                                                                     \   \7 //            \   \7 //                                            \   \7 //                                                                               \   \7 //

$$\left(\left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)}\right) + \left(\left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \pi\right) + \left(\left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}\right) + \left(- i \log{\left(- \left(-1\right)^{\frac{3}{14}} \right)} + \left(- i \log{\left(- \sqrt[14]{-1} \right)} + \left(\left(\left(\left(\left(\left(\left(- \frac{\pi}{2} - \frac{3 \pi}{14}\right) - \frac{\pi}{14}\right) + \frac{\pi}{14}\right) + \frac{3 \pi}{14}\right) + \frac{\pi}{2}\right) + \frac{11 \pi}{14}\right) + \frac{13 \pi}{14}\right)\right)\right)\right)\right)\right) + \left(- i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}\right)$$

                                                   /    _____________________\
12*pi        / 14____\        /     3/14\          |   /    2/pi\      2/pi\ |
----- - I*log\-\/ -1 / - I*log\-(-1)    / - 4*I*log|  /  cos |--| + sin |--| |
  7                                                \\/       \7 /       \7 / /

$$- i \log{\left(- \sqrt[14]{-1} \right)} - i \log{\left(- \left(-1\right)^{\frac{3}{14}} \right)} - 4 i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \frac{12 \pi}{7}$$

producto

                                                                             /                                             /   /pi\\\ /         /   /pi\\                                   \ /      /   /pi\\                                   \ /                                         /   /pi\\\
                                                                             |           /    _____________________\       |cos|--||| |         |cos|--||        /    _____________________\| |      |cos|--||        /    _____________________\| |       /    _____________________\       |cos|--|||
-pi  -3*pi -pi  pi 3*pi pi 11*pi 13*pi /      / 14____\\ /      /     3/14\\ |           |   /    2/pi\      2/pi\ |       |   \7 /|| |         |   \7 /|        |   /    2/pi\      2/pi\ || |      |   \7 /|        |   /    2/pi\      2/pi\ || |       |   /    2/pi\      2/pi\ |       |   \7 /||
----*-----*----*--*----*--*-----*-----*\-I*log\-\/ -1 //*\-I*log\-(-1)    //*|-pi - I*log|  /  cos |--| + sin |--| | + atan|-------||*|pi - atan|-------| - I*log|  /  cos |--| + sin |--| ||*|- atan|-------| - I*log|  /  cos |--| + sin |--| ||*|- I*log|  /  cos |--| + sin |--| | + atan|-------||
 2     14   14  14  14  2    14    14                                        |           \\/       \7 /       \7 / /       |   /pi\|| |         |   /pi\|        \\/       \7 /       \7 / /| |      |   /pi\|        \\/       \7 /       \7 / /| |       \\/       \7 /       \7 / /       |   /pi\||
                                                                             |                                             |sin|--||| |         |sin|--||                                   | |      |sin|--||                                   | |                                         |sin|--|||
                                                                             \                                             \   \7 /// \         \   \7 //                                   / \      \   \7 //                                   / \                                         \   \7 ///

$$- i \log{\left(- \left(-1\right)^{\frac{3}{14}} \right)} - i \log{\left(- \sqrt[14]{-1} \right)} \frac{13 \pi}{14} \frac{11 \pi}{14} \frac{\pi}{2} \frac{3 \pi}{14} \frac{\pi}{14} \cdot - \frac{\pi}{14} \cdot - \frac{\pi}{2} \left(- \frac{3 \pi}{14}\right) \left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}\right) \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \pi\right) \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)}\right) \left(- i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}\right)$$

          12    / 14____\    /     3/14\
2606175*pi  *log\-\/ -1 /*log\-(-1)    /
----------------------------------------
             1157018619904

$$\frac{2606175 \pi^{12} \log{\left(- \sqrt[14]{-1} \right)} \log{\left(- \left(-1\right)^{\frac{3}{14}} \right)}}{1157018619904}$$

2606175*pi^12*log(-(-1)^(1/14))*log(-(-1)^(3/14))/1157018619904

Respuesta rápida [src]

     -pi 
x1 = ----
      2

$$x_{1} = - \frac{\pi}{2}$$

     -3*pi
x2 = -----
       14

$$x_{2} = - \frac{3 \pi}{14}$$

     -pi 
x3 = ----
      14

$$x_{3} = - \frac{\pi}{14}$$

     pi
x4 = --
     14

$$x_{4} = \frac{\pi}{14}$$

     3*pi
x5 = ----
      14

$$x_{5} = \frac{3 \pi}{14}$$

     pi
x6 = --
     2

$$x_{6} = \frac{\pi}{2}$$

     11*pi
x7 = -----
       14

$$x_{7} = \frac{11 \pi}{14}$$

     13*pi
x8 = -----
       14

$$x_{8} = \frac{13 \pi}{14}$$

           / 14____\
x9 = -I*log\-\/ -1 /

$$x_{9} = - i \log{\left(- \sqrt[14]{-1} \right)}$$

            /     3/14\
x10 = -I*log\-(-1)    /

$$x_{10} = - i \log{\left(- \left(-1\right)^{\frac{3}{14}} \right)}$$

                                                   /   /pi\\
                 /    _____________________\       |cos|--||
                 |   /    2/pi\      2/pi\ |       |   \7 /|
x11 = -pi - I*log|  /  cos |--| + sin |--| | + atan|-------|
                 \\/       \7 /       \7 / /       |   /pi\|
                                                   |sin|--||
                                                   \   \7 //

$$x_{11} = - \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}$$

               /   /pi\\                                   
               |cos|--||        /    _____________________\
               |   \7 /|        |   /    2/pi\      2/pi\ |
x12 = pi - atan|-------| - I*log|  /  cos |--| + sin |--| |
               |   /pi\|        \\/       \7 /       \7 / /
               |sin|--||                                   
               \   \7 //

$$x_{12} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \pi$$

            /   /pi\\                                   
            |cos|--||        /    _____________________\
            |   \7 /|        |   /    2/pi\      2/pi\ |
x13 = - atan|-------| - I*log|  /  cos |--| + sin |--| |
            |   /pi\|        \\/       \7 /       \7 / /
            |sin|--||                                   
            \   \7 //

$$x_{13} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)}$$

                                               /   /pi\\
             /    _____________________\       |cos|--||
             |   /    2/pi\      2/pi\ |       |   \7 /|
x14 = - I*log|  /  cos |--| + sin |--| | + atan|-------|
             \\/       \7 /       \7 / /       |   /pi\|
                                               |sin|--||
                                               \   \7 //

$$x_{14} = - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}$$

x14 = -i*log(sqrt(sin(pi/7)^2 + cos(pi/7)^2)) + atan(cos(pi/7)/sin(pi/7))

Respuesta numérica [src]

x1 = -7.85398156908478

x2 = 84.1498032211552

x3 = -72.0322315573088

x4 = -55.875469338847

x5 = 18.1763574957695

x6 = 46.0018924275648

x7 = -81.905808468591

x8 = 14.1371666781978

x9 = -80.1106127288493

x10 = -39.7187071203852

x11 = -37.9235113183339

x12 = -29.8451301480097

x13 = -67.9930410026934

x14 = 86.3937983040671

x15 = 40.1675060708981

x16 = -25.8059396544876

x17 = -19.9715532978208

x18 = -61.7098556955138

x19 = 32.0891249616672

x20 = -73.8274272888222

x21 = -98.0625706870528

x22 = 74.276226309873

x23 = 54.0802735367957

x24 = 0.224399475256414

x25 = 2.01959527730772

x26 = -3.81479107935903

x27 = 64.4026491723469

x28 = -54.5290724873086

x29 = 50.0410829821803

x30 = 10.0979763865386

x31 = 42.4115010150339

x32 = 52.7338766852572

x33 = -33.8843207637185

x34 = 88.1889937757706

x35 = 58.1194639733282

x36 = -76.0714221119243

x37 = -10.9955743995035

x38 = -21.7667490998721

x39 = -83.7010042706423

x40 = 4.26359002987186

x41 = 96.2673748850015

x42 = 92.6769831195842

x43 = 19.9715532978208

x44 = 94.0233801324374

x45 = -32.9867228544314

x46 = 67.9930410026934

x47 = 24.0107438524363

x48 = 388.884290619365

x49 = -69.7882368047447

x50 = -91.7793853798732

x51 = 6.05878583192317

x52 = 80.1106126783847

x53 = -51.8362787100334

x54 = -15.9323627432054

x55 = 62.1586546460266

x56 = 66.1978452006421

x57 = -11.8931721885899

x58 = -50.0410829821803

x59 = -46.0018924275648

x60 = -6.05878583192317

x61 = -63.9538504480779

x62 = 70.2370357552575

x63 = 89.9841895778219

x64 = 98.0625706870528

x65 = 35.6795165657698

x66 = -58.1194641568646

x67 = 92.2281843303861

x68 = 22.215548050385

x69 = -28.0499344070517

x70 = -47.7970882296161

x71 = 48.245887180129

x72 = -41.9627018729494

x73 = -43.7578976750007

x74 = -5.60998688141034

x75 = -17.7275585452567

x76 = 54.9778717349604

x77 = -89.9841895778219

x78 = 76.0714221119243

x79 = -24.0107438524363

x80 = 72.0322315573088

x81 = 26.2547386050004

x82 = -65.7490462501292

x83 = -87.7401948252578

x84 = -77.8666179139756

x85 = -94.0233801324374

x86 = -59.9146598934625

x87 = 58.1194639815683

x88 = 28.0499344070517

x89 = 100.306565439617

x90 = -85.9449990232065

x91 = -95.8185758715514

x92 = -2.01959527730772

x93 = -99.8577664891041

x94 = 44.2066966255135

x94 = 44.2066966255135

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Expresiones idénticas

Expresiones semejantes

cos4xcos2x=sin3xsin5x la ecuación

Solución numérica:

Solución